4MA0 Higher January 2014 Paper 3R Q15
15 A particle moves along a straight line.
The fixed point \(O\) lies on this line.
The displacement of the particle from \(O\) at time \(t\) seconds is \(s\) metres, where \[s = t^3 - 6t + 3\]
(a) Find an expression for the velocity, \(v\) m/s, of the particle at time \(t\) seconds. (2)
(b) Find the acceleration of the particle at time 5 seconds.
.................... m/s2 (2)
.................... m/s2 (2)
| Scheme | Marks |
|---|---|
| \(3t^2 - 6\) | B2 |
| (2) |
Notes
B2: for \(3t^2 - 6\)
B1 for two of three terms differentiated correctly
| Scheme | Marks |
|---|---|
| \(6t\) | M1 |
| 30 | A1 |
| (2) | |
| (4 marks) |
Notes
M1: ft from quadratic (a)